Differential Equation Model for the Ground to First 2+ State Excitation Energy E2 of Even-Even Nuclei

TL;DR

This paper introduces a novel differential equation model for predicting the excitation energy E2 of the first 2+ state in even-even nuclei, based on derivatives with respect to neutron and proton numbers, validated with nuclear data.

Contribution

The paper develops a new differential equation model for E2 energy, linking it to derivatives of neighboring nuclei, and derives recursion relations for practical predictions.

Findings

Recursion relations accurately predict E2 values across the nuclear chart.

Model's predictions align well with existing experimental data.

Potential to estimate unknown E2 energies in nuclei.

Abstract

We propose here a new model termed as the Differential Equation Model for the ground to first 2+ state excitation energy E2 of a given even-even nucleus, according to which the energy E2 is expressed in terms of its derivatives with respect to the neutron and proton numbers. This is based on a similar derivative equation satisfied by its complementary physical quantity namely the Reduced Electric Quadrupole Transition Probability B(E2) in a recently developed model. Although the proposed differential equation for E2 has been perceived on the basis of its close similarity to B(E2), its theoretical foundation otherwise has been clearly demonstrated. We further exploit the very definitions of the derivatives occurring in the differential equation in the model to obtain two different recursion relations for E2, connecting in each case three neighboring even-even nuclei from lower to higher mass numbers and vice-verse. We demonstrate their numerical validity using the available data throughout the nuclear chart and also explore their possible utility in predicting the unknown E2 values.